Positive periodic solutions for second order impulsive differential equations

• Autorzy: Shen J. , Wang W. , He Z.
• Języki publikacji: EN

Abstrakty

EN

The existence of positive periodic solutions for a class of second order impulsive differential equations is studied. By using fixed point theorem in cone, new existence results of positive periodic solutions are obtained without assuming the existence of positive periodic solutions of the corresponding continuous equation.

Słowa kluczowe

EN

impulsive differential equation; periodic solution; fixed-point theorem

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2011
• Tom: Vol. 44, nr 2
• Strony: 297--316
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Shen J.

• Department of Mathematics Hangzhou Normal University Hangzhou, Zhejiang 310036, P.R. China

autor

Wang W.

• Department of Mathematics Hunan University of Science and Technology Xiangtan, Hunan 411201, P.R. China

autor

He Z.

• College of Science Zhejiang Forestry University Hangzhou, Zhejiang 311300, P.R. China

Bibliografia

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• [3] W. Ding, J. Mi, M. Han, Periodic boundary value problems for the first order impulsive functional differential equations, Appl. Math. Comput. 165 (2005), 443–456.
• [4] W. Ding, M. Han, Periodic boundary value problem for the second order impulsie functional differential equations, Appl. Math. Comput. 155 (2004), 709–726.
• [5] Z. He, J. Yu, Periodic boundary value problem for first order impulsive functional differential equations, J. Comput. Appl. Math. 138 (2002), 205–217.
• [6] V. Lakshmikantham, D. D. Bainov, P. S. Simeonov, Theory of Impulsive Differentia Equation, Singapore: World Scientific, 1989.
• [7] Y. Li, Q. Zhou, Periodic solutions to ordinary differential equations with impulses, Sci. China Ser. A 36(7) (1993), 778–790.
• [8] Y. Li, Positive periodic solutions of first and second order ordinary differential equations, Chinese Ann. Math. 25(B) (2004), 413–420.
• [9] J. Li, J. Shen, Periodic boundary value problems for second order differential equations with impulses, Nonlinear Stud. 12(4) (2005), 391–400.
• [10] D. Guo, Periodic boundary value problem for second order impulsive integro-differential equation in Banach space, Nonlinear Anal. 8(6) (1997), 709–726.
• [11] D. Guo, V. Lakshmikantham, Nonlinear Problem in Abstract Cones, Academic Press, New York, 1988.
• [12] J. Yu, W. Ge, Nonlinear boundary value problem of differential equations with impulsive effects, Math. Appl. 14(3) (2001), 116–120.